Answer to Question #300054 in Algebra for Michael

Question

Solve for x when a,b and c are negative constants

1. (ax+b)/c≤b

2. If a>1 then prove that a²>1

Answer 1

1.(ax+b)/c≤b

ax+b≥bc

ax≥bc-b

x≤(bc-b)/a

2. If a>1 then a-1>0

Let's check a²-1=(a-1)(a+1)

a-1>0 and a+1>0

In this way a²-1>0 ⇒ a²>1